1. Field of the Invention
The present invention relates to methods and apparatus for manifesting a characteristic or regularity, which is latent and can not ordinarily be recognized by visual inspection, although such characteristic or regularity actually exists in a complicated symbolic sequence, for example, a nucleotide sequence of DNA, an amino acid sequence of a protein, or a digital sequence of decimal expansion of an irrational number and the like. In these sequences, regularity can not be recognized at a glance even when regularity exists therein. The present invention enables recognition of a characteristic or regularity existing within a symbolic sequence, which has not yet been recognized.
2. Description of the Related Art
Some complicated symbolic sequences contain a characteristic, which has not been recognized by human beings, although the characteristic actually exists. For example, genetic information is represented by a long sequence of symbols. The symbols consist of four different symbols, each indicating one of the four types of nucleotides. A large number of symbols are one-dimensionally aligned. In the study of genetic information, it is extremely important to recognize a certain regularity hidden within the symbolic sequence that represents the genetic information. In addition, if a certain regularity is found in an irrational number, e.g., the number π, and the base of natural logarithm (e), the study of irrational numbers will be enhanced and various developments can be expected in mathematics.
For such purpose, various efforts have been made to analyze a symbolic sequence based on a variety of mathematical methods, such as Fourier analysis. However, these efforts have not necessarily accomplished successful results. One problem with conventional analysis methods is that, even if a certain regularity exists within a portion of a very long symbolic sequence, the latent regularity is buried within the entire sequence and can not be recognized when the entire symbolic sequence is analyzed. Since there has been no effective technology for determining in advance as to which part of the sequence that the regularity exists, there are many characteristics or regularity which can not be recognized by conventional analysis methods.